Investigating efficiency of Adomian decomposition method in solving van der pol’s equation compared to regular perturbation method
Wambugu Jane Wanjiku, Dr. John Njenga, Professor Gatoto James
Many physical systems are mathematically modeled leading to nonlinear ordinary differential equations or partial differential equations, raising the need for an effective method for analyzing the mathematical models which provide solutions that conform to physical problems. The Adomian Decomposition Method (ADM) has been used to solve a wide range of dynamical systems since its introduction in 1980’s. Nonlinear oscillatory differential equations have been used in modeling many dynamical systems and they demonstrate many basic properties of nonlinear systems. These equations have been solved using many approximations methods e.g. Differential transform, perturbation, variation iteration, and Lindstedt methods. This work investigates the efficiency in the application of ADM versus perturbation method in solving one of the nonlinear oscillatory differential equations, the Van Der Pol’s equation. For analysis of accuracy, Runge- Kutta fifth order method is used as a comparison criterion and respective error bounds are obtained. These results will enhance confidence in the application of ADM or perturbation method in solving nonlinear oscillatory systems.